Anakin doesn't bat an eyelash-- it's not like he's never gone undercover, and it's not something uncommon in his family and the people close to it.

"I've been both. Plus, my mom's a politician. Sometimes I need to know so I don't make her or the Jedi look bad."

Granted, with the general public attitude toward Jedi lately, he could be a perfect guest and still offend.